Newton's Second Law and determines how the wavefunction evolves with time. The diffraction phenomenon observed for electrons suggests that electron states with definite momenta should behave like propagating waves, with wavelength inversely proportional to the momentum and frequency proportional to the kinetic energy. By postulating that the wavefunctions for momentum eigenstates behave in this way, we will arrive at an evolution equation for wavefunctions known as the "Schrodinger equation" [1]. This is the general equation for the time evolution of quantum states, and the remainder of the course will be spent exploring its consequences. Bound states and atomic spectra We will first study the Schrodinger equation for particles that are classically trapped in a finite region of space due to external forces. An example is an electron in an atom whose energy is less than the amount required to overcome the Coulomb attraction of the nucleus. We will see that in these cases, the Schrodinger equation implies that the particle can exist only at certain specific energies. This explains the discrete nature of atomic spectra: electrons can absorb or emit energy only in the precise amounts that allow them to jump between their allowed energies. Tunnelling One of the surprising consequences of the Schrödinger equation is that particles have some probability of being found in places where the classical potential energy is greater than the total energy of the particle. A result of this is that particles can pass through barriers created by external forces that would classically block them completely. This phenomenon can be used to understand certain types of radioactive decay and is central to a number of important technological applications, such as scanning-tunnelling electron microscopes that are able to see individual atoms. It is also possible that the whole Universe appeared through a tunnelling phenomenon! Learning Goals The following is a list of learning goals for the course. These are things you should know or be able to do once we have covered each topic. Broad Goals After taking this course, students should be able to do the following. . State the principle of relativity, and be able to describe some of the basic implications of this that go against our usual intuition (and explain how experimental evidence supports these).